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Find the inverse of y = 2x+1/ x-1

the aim of finsing the inverse is making x the subject. To start we need to multiply both sides by: (x-1), giving us:

y(x-1) = 2x+1

now we need to expand the brackets:

yx - y = 2x+1

now gather all the x components on the same side:

yx-2x = 1+y

now factorise the left hand side:

x(y-2) = 1+y

now make x the subject, giving us:

x = 1+y/ y-2

therefore, the inverse is written in terms of x, which gives us:

f(x)^-1 = 1+y/y-2

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